{
  "id": "2310.04067",
  "version": "v1",
  "published": "2023-10-06T07:49:41.000Z",
  "updated": "2023-10-06T07:49:41.000Z",
  "title": "Spectral analysis of the discrete Maxwell operator: The limiting absorption principle",
  "authors": [
    "Olivier Poisson"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We are interested by the spectral analysis of the anisotropic discrete Maxwell operator $\\hat H^D$ defined on the square lattice $\\rm Z\\!\\!\\! Z^3$. In aim to prove that the limiting absorption principle holds we construct a conjugate operator to the Fourier series of $\\hat H^D$ at any not-zero real value. In addition we show that at some particular thresholds the conjugate operator is essentially self-adjoint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-06T07:49:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral analysis",
      "anisotropic discrete maxwell operator",
      "conjugate operator",
      "limiting absorption principle holds",
      "not-zero real value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}